Much of the analysis of economic growth has focused on the study of aggregate output. Here, we deviate from this tradition and look instead at the structure of output embodied in the network connecting countries to the products that they export. We characterize this network using four structural features: the negative relationship between the diversification of a country and the average ubiquity of its exports, and the non-normal distributions for product ubiquity, country diversification and product co-export. We model the structure of the network by assuming that products require a large number of non-tradable inputs, or capabilities, and that countries differ in the completeness of the set of capabilities they have. We solve the model assuming that the probability that a country has a capability and that a product requires a capability are constant and calibrate it to the data to find that it accounts well for all of the network features except for the heterogeneity in the distribution of country diversification. In the light of the model, this is evidence of a large heterogeneity in the distribution of capabilities across countries. Finally, we show that the model implies that the increase in diversification that is expected from the accumulation of a small number of capabilities is small for countries that have a few of them and large for those with many. This implies that the forces that help drive divergence in product diversity increase with the complexity of the global economy when capabilities travel poorly.